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As @Nadrak and @afriedman1337b14a_ESO said, you can get honing stones from deconstructing items and refining ore. You can increase the chance by spending points in blacksmithing (there's a skill but I can't remember the name of it right now)
As others have said but also from the hirelings. I am spending this early access period to get 5-6 alts to the point where they can have a skill point in hireling for blacksmithing, clothing and woodworking. I'm hoping this will lead to a steady stream of useful mats every day (already snagged the blue quality blacksmithing oil by doing this).